Timeline for Enumerating all Hamiltonian Cycles in a Bipartite Vertex Transitive Graph
Current License: CC BY-SA 3.0
6 events
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| Nov 29, 2011 at 17:55 | comment | added | Ng Yong Hao | Interesting. I guess I will try to find the error when I have the time then. As for the preprint, I am fine to wait for the actual paper to be available online. After all, I am quite interested to play around with the problem to see how far I can go. Thanks for your assistance again! | |
| Nov 27, 2011 at 18:32 | comment | added | Patric Ostergard | The mentioned arxiv paper (which is actually not a paper but rather an announcement of a couple of numbers) is in error. Actually, it is a nice little problem for students in a combinatorics class to show how one can deduce the incorrectness based on the few tiny bits of information provided in the paper/announcement. I have informed OEIS about our new results. | |
| Nov 26, 2011 at 8:29 | comment | added | Ng Yong Hao | Also, I noticed that there is another paper on [Hamiltonian cycles in 6-cube][1] It appears that their result of 14754666508334433250560 Hamiltonian cycles (directed) is recorded in [OEIS A066037][2] It seems to me that this is the also the question that your paper is addressing. Perhaps there are some miscalculations for their values? My apologies if I made any mistakes here. [1]: arxiv.org/abs/1003.4391 [2]: oeis.org/A066037/internal | |
| Nov 25, 2011 at 13:46 | comment | added | Ng Yong Hao | Many thanks for the information! From my experiments fixing 30/70 vertices reduces the brute force to instantaneous. With a number of symmetries I felt that $n=7$ should be doable. Nothing better than a confirmation though. Like what you mentioned, I found a lot of symmetries each only applicable to specific sequences. I am planning the pseudocode at the moment, actual program will probably take a while. Do you think the effort, mainly on the exploration of the symmetries, will be meaningful enough to be put into a paper? (seeing this is a rather specific case) | |
| Nov 25, 2011 at 12:44 | vote | accept | Ng Yong Hao | ||
| Nov 24, 2011 at 20:34 | history | answered | Patric Ostergard | CC BY-SA 3.0 |